1. Field of Invention
The present invention relates to seismic exploration, and more particularly refraction tomography. A specific example is for correction of near-surface anomalies.
2. Description of the Prior Art
An important problem in seismic exploration is that of distortions in seismic images due to near-surface velocity anomalies. Therefore, the analysis of refraction data for statics estimation to reveal information about the near surface, and correspondingly about statics, is very important in seismic processing.
Near-surface velocity anomalies produce severe distortions in seismic images. If one knew the structure of these anomalies, the best way to tackle this problem would be to perform wave-equation datuming or depth migration from the surface through the known structure. However, 3-D prestack depth imaging and datuming are computational challenges. Therefore, statics applications assuming surface-consistent ray propagation through the near surface have remained the main tool to account for near-surface anomalies.
The analysis of the stacking responses of reflection data works better for estimating the short-period part of statics (so called residual statics), while estimation of the long-period statics using reflection data alone is very unstable and inefficient. Therefore, analysis of refraction data for statics estimation to reveal more information about the near surface, and correspondingly about statics, is customary in conventional seismic processing.
The generalized reciprocal method has been widely applied to 2-D data. Unfortunately, for 3-D seismic the reciprocal method is difficult to apply due to the lack of reciprocal data. The idea of delay times also appeared useful for 3-D refraction statics calculations. The delay-time method assumed a near-surface model of locally flat layers on the scale of offset range. First arrivals were assumed to be the onset of head waves propagating along refracting interfaces of these layers. First arrival pick times were decomposed into delay times and refracting-layer velocities. Delay times were then converted to layer thicknesses and velocities assuming a critical angle of incidence on the refracting layers. A technique known as Refraction MISER(copyright) available from the assignee of the present application is an example of the delay time method.
The delay-time method is also used in other approaches, such as Generalized Linear Inversion (GLI) and head-wave refraction tomography. In these methods, instead of the two-step inversion via delay times, traveltimes were inverted directly for layer thicknesses and velocities. However, these methods also had to deal with the problem of velocity/depth ambiguity. To address this issue, it was common practice to fix the weathering velocity prior to depth estimation. Incorporation of reflection data for joint inversion with refraction data could at times reduce the velocity/depth ambiguities. Unfortunately, near-surface reflections were very difficult to pick in normal production data.
One of the main problems with head-wave methods has been that in areas with complex geology and rough terrains the simple model typically employed was not sufficient to explain important data features. Moreover, in order to fit the observed nonlinear move out of first arrivals one had to either limit the offset range or include more layers in the model. Both approaches made inversion even more unstable and ambiguous.
Theoretical amplitudes of head waves have been expected to be several orders of magnitude less than body waves, and therefore head waves should be poorly represented in the data. On the other hand, even a small positive vertical velocity gradient could produce a variety of interference waves or modes that included diving (turning) waves with much larger amplitudes than head waves. The kinematics of diving waves are nonlinear. In most cases, diving-wave modeling fitted the observed first-arrival moveouts better than head-wave modeling.
The reasons discussed above made diving-wave tomography, assuming first arrivals as on-sets of diving waves, a very attractive alternative to head-wave methods for statics calculation. In this approach the medium was parameterized as a number of cells, diving rays were traced through the model, and traveltime residuals were backprojected or inverted for slowness perturbations in every cell crossed by rays. Since diving waves fitted the nonlinear moveout of first arrivals better than head waves, broader offset ranges could be included for processing, reducing ambiguity in the inversion. However, limiting the incidence-angle aperture at the weathering layer still made inversion for parameters of this layer ambiguous. Another problem with tomography was the huge number of unknowns, especially for 3-D surveys. This has required special efforts to make the inversion feasible and stable.
Previous tomographic approaches have used head waves and diving waves. Head-wave based methods have in general been robust because the model parameters depend almost linearly on the observed traveltimes. In contrast, diving-wave based methods incorporated a wider offset range, and the relationship between the model parameters and the traveltimes became nonlinear because of a significant dependence of the processing on the assumed ray paths. This has made tomographic results sensitive to the initial model. The tomographic solution could be stabilized by using a Fourier parameterization, but the solution remained sensitive to the initial model because of the use of ray tracing.
Refraction tomography would be more desirable, if one were able to remove the initial model dependency due to ray tracing. It has been shown that traveltime inversion possesses an inherently linear formulation in the tau-p domain. However, practical implementation of the tau-p transform for traveltimes has not been straightforward, especially for the case of 3-D survey data.
Other approaches have been proposed for avoiding ray tracing in tomography. These methods used a spatial traveltime decomposition constrained by the eikonal equation. The eikonal method was based on a vertical seismic profile and cross-hole transmission geometry. Although well suited for vertical seismic profiling and cross-hole geometries, these techniques were difficult to apply to refraction data.
It can thus be seen that the conventional cell parameterization used in tomography was, so far as is known, generally ineffective for modeling near-surface geological structures. Further, it introduced a large number of unknowns. In the cell-based formation, the tomographic problem was ill-posed and required a regularization that was not straightforward. Furthermore, the quality of the initial model required for ray tracing and nonlinear inversion depended on an analysts expertise, and this could ultimately lead to a bias in the final solution.
Briefly, the present invention performs refraction tomography of seismic data using differential delay times. According to the present invention, seismic data obtained during a seismic survey from a plurality of seismic stations are processed to remove the effect of statics from the data. Traveltime/offset functions are formed for the seismic stations from first-arrival picks obtained from the data. The traveltime/offset functions are transformed into velocity/depth functions to derive a near-surface model. Long-period statics in the data are then determined from the derived near-surface model. Short-period statics are estimated by surface-consistent decomposition of the traveltime residuals. The determined long-period and short-period statics are then removed from the seismic data, which are then available for display or subsequent processing in order to be analyzed.
The techniques of the present invention estimate the near surface velocity model and produce static corrections by means of first-break traveltime tomography without ray tracing. The traveltime inversion implemented according to the present invention involves several steps. First, the data are selected for inversion from a specified offset range and adjusted, if necessary. Then, a 3-D function is estimated from first-arrival picks using a method combining 1-D modeling and nonparametric regression. Next, differential delay times are used for calculation of local velocity/depth functions that make up the near-surface model. Then, long-period statics are calculated using the derived model, Short-period statics are estimated by surface-consistent decomposition of the traveltime residuals. The short-period and long-period statics may then be removed from the seismic data.
The present invention combines an approach of unconstrained spatial traveltime decomposition with a linear inversion in tau-p domain. The present invention performs no explicit ray tracing. The approach used combines the robustness of head-wave (delay-time) methods, as it does not require an initial model or ray tracing, and the flexibility of diving-wave tomography, as it inverts both head and diving waves over the complete offset range.